Simplify the following expression: $t = \dfrac{-6z^2 - 12z + 288}{z + 8} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-6$ , so we can rewrite the expression: $ t =\dfrac{-6(z^2 + 2z - 48)}{z + 8} $ Then we factor the remaining polynomial: $z^2 + {2}z {-48} $ ${8} {-6} = {2}$ ${8} \times {-6} = {-48}$ $ (z + {8}) (z {-6}) $ This gives us a factored expression: $\dfrac{-6(z + {8}) (z {-6})}{z + 8}$ We can divide the numerator and denominator by $(z - 8)$ on condition that $z \neq -8$ Therefore $t = -6(z - 6); z \neq -8$